Application of differential equation help!!

[madoscar65]

Hi peoples,
I need a little help with an extended response questions...
Two chemicals, A and B, are put together in a solution where they react form a compound, X. The rate of increase of the mass, x kg, of X is proportional to the proudct of the masses of unreacted A and B present at time t minutes. it takes 1 kg of A and 3 kg of B to form 4kg of X. Initially 2 kg of A and 3kg of B are put together in solution. One kg of X forms in one minute.

a. Set up the appropriate differential equation expressing dx/dt as a function of x.

So firstly, I know dx/dt = kAB, and I need to find A and B in terms of x.. " It takes 1 Kg of A and 3Kg of B to form 4kg of X" I can't seem to intepret this information into mathsmatical equation.. So hope you guys can help me out

Thanks in advance!!

[kamil9876]

Suppose that x kg of X are produced. That means that:

(1) kg of A must've been consumed, so we have

(2) kg of B must've been consumed, so we have

Now sub back in.

[madoscar65]

Thanks +1 Karma